If you are taking photos of fast-moving subjects, and the subjects are blurry, there are a few potential causes:
- Use of a lens that is to slow
- An f/3.5-5.6 aperture is SLOW
- An f/2.8 or wider aperture is faster
- Use of a lens that does not have IS
- Image stabilization helps eliminate camera shake blur
- Use of a camera that lacks adequate AF capabilities
- Better AF systems help you nail focus and keep it nailed as you track a moving subject
- Use of camera settings that are inadequate
- Using a shutter speed lower than 1/focalLength is often too low
- Use of poor panning technique
- Panning can be tricky, and poor technique can introduce blur
From a gear recommendation standpoint, I would first look into a better lens. The 18-55mm f/3.5-5.6 kit lens is pretty slow. If you are taking photos of skiers, your probably at 55mm, in which case your aperture is f/5.6. Thats quite slow, and probably forcing you to use a slower shutter speed than necessary to stop motion effectively. The AF system of the Canon T3 is not that great either, and while it is capable of basic subject tracking, your likely to have a low ratio of keepers. With a better/faster lens, you should be able to make more effective use of your camera's AF system, so I would still look into a better lens first.
If I was to recommend a few specific lenses that might help, they would be the EF-S 17-55mm f/2.8 lens, or the EF-S 18-200mm f/3.5-5.6 lens. The former has a nice wide aperture at all focal lengths, and the latter has great IS to make up for the narrower aperture. For shooting action, having a longer focal length up to 200mm can be very useful, and with decent IS, you should still be able to get nice shots at 200/5.6.
Shooting technique is another factor that can affect sharpness. Practice your panning as much as you can. Practice it both hand-held, and with a tripod or a monopod, as eliminating vertical shake can help eliminate blur from camera shake. When shooting fast subjects, you want to use fast shutter speeds. As a general rule of thumb, a shutter speed of 1/focalLength is necessary (without IS) to get a sharp shot, although that may change with high speed subjects.
When it comes to technique, properly using an AF system is one of the most important. If you are shooting moving subjects, especially high speed ones, you will not only want to hone your panning skills...you'll want to learn how to use the AF system. The T3 has a 9 point AF system with a single cross-type sensor in the center. Its not the most capable system, but it should do what you need until your skill grows beyond its capabilities (which, depending on how good a learner you are, may be soon, or may take a year or two. If you DO run into the AF systems limitations, the Canon 7D offers an excellent AF system, high frame rate, and a lot of customizability at around $1400 right now.)
First thing you'll want to do when you get out to shoot the action, particularly with the longer focal lengths you will likely find necessary (i.e. 200mm), you will want to switch to AI Servo mode. Single shot mode is inadequate to properly track subjects in motion frame-to-frame. AI Servo mode will continually adjust focus to keep a subject it has locked on to in focus so long as its tracking it. When you press the shutter button half-down, AF will initiate. Once its locked on, you should be able to fully press the shutter button, to take a shot, and release to half-way again to continue AF. Keeping your subject under the center point will improve AF performance.
When photographing high speed subjects in lateral motion, however, you often need much higher shutter speeds...even with IS. Birds are my favorite in-motion subject, and I often need a shutter speed higher than 1/1000th to capture subjects with minimal motion blur in some areas (i.e. wing tips), and 1/1600th or more to completely freeze motion. I would expect similar needs for photographing high speed skiers and snowboarders. As a general rule for action, ether use Tv mode, auto ISO, and pick a fixed shutter speed, or use Av, set a high ISO setting...such as ISO 800-1600, and let the camera pick the shutter speed for you. With a high enough ISO setting, the camera should pick an appropriate shutter speed to freeze motion most, if not all, of the time.
From an artistic standpoint, a bunch of technobable about shutter speeds and ISO settings are not going to help you as much. Some experimentation will be necessary to get the artistic effect you want. If you want to guarantee a certain amount of motion blur in your shots, you will probably want to use Tv mode, wither with auto ISO, or a fixed ISO setting that you know will ensure a proper exposure, and let the camera vary aperture for you. You may only need a shutter speed of 1/500th and an ISO of 400 to get just the right amount of motion blur into each shot.
On the flip side, you may want to keep your DOF as thin as possible. In that case, using Av mode at or near max aperture with a high ISO should ensure the camera selects a high enough shutter speed. Depth of field will be dependent on aperture and subject distance, and unless you have an f/2.8 normal or f/4-5.6 telephoto lens, you might need to get close to your subjects to keep your dof thin...blurring backgrounds.
Don't Fear the Gear!
Finally, you may simply find after some experimentation that a single semi-automatic setting doesn't meet your needs. In that case, don't be afraid to switch to full manual mode, and adjust your settings as the moment demands. And DON'T be afraid to use higher ISO settings...if they are necessary to support a high shutter speed, crank it up!